In this paper, on quantum Ising model dynamics, they consider the Hamiltonian
$$\mathcal{H} = \sum_{j < k} J_{jk} \hat{\sigma}_{j}^{z}\hat{\sigma}_{k}^{z}$$
and the correlation function
$$\mathcal{G} = \langle \mathcal{T}_C(\hat{\sigma}^{a_n}_{j_n}(t_n^*)\cdot\cdot\cdot...
I've read these two pages that discuss going from qubit to continuous variable - https://arxiv.org/abs/quant-ph/0008040 and https://arxiv.org/abs/1907.09832 . I'm curious if anyone knows some papers that discuss going the other way around? I.e. qubitizing a continuous variable model? Any insight...
Consider a VCSEL laser that emits photon pulses with Poisson distribution for the number of photons per pulse. The power of the VCSEL has been set low so the mean photon number "u" is u<1. Consider this photon pulses can take two non-orthogonal states of polarization (for example: state 0 with...
Here's what I think I understand:
First off, the GHZ state ##|GHZ \rangle = \frac {|000\rangle+|111\rangle} {\sqrt 2}##, and ##\sigma_x## and ##\sigma_y## are the usual Pauli matrices, so the four operators are easy to calculate in Matlab.
I'm thinking the expectation values of each operator...
Am I correct in thinking that the system measures the probability |<f|1>|^2 for some state <f|? Then the probabilities for each of the six states would be:
|<0|1>|^2= 0
|<1|1>|^2= 1
|<+x|1>|^2= |(1/√2)|^2 = 1/2
|<-x|1>|^2= |(-1/√2)|^2 = 1/2
|<+y|1>|^2= |(-i/√2)|^2 = 1/2
|<-y|1>|^2= |(i/√2)|^2...
Part a:
Gate
H
X
Y
Z
S
T
R_x
R_y
Theta
pi
pi
pi
pi
pi/2
pi/4
pi/2
pi/2
n_alpha
(1/sqrt(2))*(1,0,1)
(1,0,0)
(0,1,0)
(0,0,1)
(0,0,1)
(0,0,1)
(1,0,0)
(0,1,0)
Using the info from the table and equation 1, I find:
U_H=(i/sqrt(2))*[1,1;1,-1]
U_X=i*[0,1;1,0]
U_Y=i*[0,-i;i,0]
U_Z=i*[1,0;0,-1]...
Given that operator ##S_M##, which consists entirely of ##Y## and ##Z## Pauli operators, is a stabilizer of some graph state ##G## i.e. the eigenvalue equation is given as ##S_MG = G## (eigenvalue ##1##).
In the paper 'Graph States as a Resource for Quantum Metrology' (page 3) it states that...
Reduced graph states are characterized as follows from page 46 of this paper:
Proposition: Let ##A \subseteq V## be a subset of vertices for a graph ##G = (V,E)## and ##B = V\setminus A## the corresponding complement in ##V##. The reduced state ##\rho_{G}^{A}:= tr_{B}(|G\rangle\langle G|)## is...
I would like to apply a General Lorentz Boost to some Multi-partite Quantum State.
I have read several papers (like this) on the theory of boosting quantum states, but I have a hard time applying this theory to concrete examples.
Let us take a ##|\Phi^+\rangle## Bell State as an example, and...
I am an undergraduate doing research on QC/QI. My current topic to learn is continuous-time quantum walks, but first I must learn the random quantum walk. That being said, I was wondering if someone could simply explain what a random quantum walk is and then explain how they could be useful with...
I have been asked to draft a (informal) research proposal for a PhD thesis. I have some background in quantum information and my interests are leaning towards the AdS/CFT correspondence. I was wondering if you could suggest a few (preferably recent) theory papers at the junction of quantum...
I have recently been reading some stuff on quantum information in the physics literature which refers to 'a mechanism by which a measurement in A determines quantum coherences in B', where A and B are subsystems of a larger system.
I am aware of the meaning of the terms 'decoherence' and...
##U_1 \otimes U_2 = (1- i H_1 \ dt) \otimes (1- i H_2 \ dt)##
We can write ## | \phi_i(t) > \ = U_i(t) | \phi_i(0)>## where i can be 1 or 2 depending on the subsystem. The ## U ##'s are unitary time evolution operators.
Writing as tensor product we get
## |\phi_1 \phi_2> = (1- i H_1 \ dt) |...
I was wondering how to measure the first or even the second qubit in a quantum computing system after for example a Hadamard Gate is applied to the system of these qubits: A|00>+B|01>+C|10>+D|11>?
A mathematical and intuitive explanation would be nice, I am a undergraduate sophomore student...
I'm having trouble understanding the phase shift produced by a beam splitter. I seem to be finding conflicting information.
I'm specifically looking to understand a 50/50 beam splitter where one side has a dielectric mirror, as shown in this figure from wikipedia:
I understand the pi...
Hello,
I am close to finishing my undergraduate degree in Computer Engineering, and I am very interested in pursuing graduate studies. For a long time, I have been passionate about computer science and I've been looking into the research done in various labs in the schools that I'm considering...
Homework Statement
J-coupling term between two spins is
HJ = ħJ/4 σz(1) σz(2)
In the measured magnetization spectrum of the spins, this leads to the splitting of the individual
spin lines by frequency J, which we’ll now derive. We can write the magnetization of spin 1 as:
<M1(t)> =...
The following, regarding quantum measurement, is stated in the paper "Limitation on the amount of accessible information in a quantum channel" :
"Our discussion of measurement will be based on a specific physical model of measurement, to which we now turn. Suppose we have a quantum system ##Q##...
I am applying to phd programs in physics right now. I am interested in doing research in quantum information science. I see there is a lot of interest and funding for quantum information science right now, but does anyone have any advice on whether or not this research will be well funded in the...
Homework Statement
I am supposed to construct a controlled Hadamard gate
using only single qubit and CNOT gates.
Homework Equations
[/B]
We know that any arbitrary unitary Operator U can be written as the Martrix product U=AXBXC, where X is the NOT-Matrix and ABC=1 (identity matrix)
I've...
I am well aware that QC-related graduate programs are competitive so I am preparing myself for a rejection. Not because I'm unconfident. But because everyone should have a backup plan just in case. I haven't applied yet because I'm about to take the GRE.
I really do enjoy both quantum physics...
Last year I've finished the undergraduate course in Mathematical-Physics and Mathematics and this year I've started on graduate school on Physics in order to obtain a master's degree. What I'm really interested are two main topics: general relativity and quantum field theory. I also like...
I am an undergraduate student in India doing my final year BS degree in Math. I am extremely interested in quantum mechanics and want to peruse quantum computation. What is the best possible course that I can take for my Masters? There appears to be a limited number of colleges that offer a...
How is information conserved when one form of energy is converted to other?
Like how a black hole's gravitational energy is used to create photon pairs near the event horizon, what happens to the information in the gravitational wavepackets (gravitons?) and how is it not lost?
Homework Statement
Prove the following relation for ##\zeta:=r e^{i \theta}##:
S(\zeta)^\dagger a S(\zeta)= a \cosh r - a^\dagger e^{i \theta} \sinh r
with ##S(\zeta)=e^{1/2[\zeta^\ast a^2-\zeta(a^\dagger)^2]}## and ##a## being the annihilation operator with eigenvalue ##\alpha##...
Homework Statement
Prove the following relations (for ##\zeta:=r e^{i\theta}##):
\begin{align}
D(\alpha)^\dagger a D(\alpha)&=a+\alpha\\
S(\zeta)^\dagger a S(\zeta)&= a \cosh r- a^ \dagger e^{i\theta} \sinh r
\end{align}
Homework Equations
##|\alpha\rangle## is the coherent state. ##a## and...
Consider a system with countable quantum states. One can define Jij as the rate of transition of probability from i-th to j-th quantum state. In H-theorem, if one assumes both $$ H:=\Sigma_{i} p_{i}log(p_{i})$$ $$J_{ij}=J_{ji}$$ then they can prove the H always decrease. The latter is Fermi's...
Hi everyone. I'm just looking for schematics of cnot quantum gate, but on the Internet it only talks about it from a mathematical point of view. I want to ask you if you have some drawing, or schematics of it, from a "Physical" implementation, in the sense, how are the spins prepared, how we...
I am a rising senior at a small liberal arts college, with an incredibly small (and therefore unrecognized) physics program. I am seeking advice regarding which Ph.D programs are within my reach. I plan on applying to AMO (Atomic, Molecular, and Optics) Ph.D programs with the intention of...
For a system consisting of multiple components, say, a spin chain consisting ofN≥3spins, people sometimes use the so-called geometric measure of entanglement. It is related to the inner product between the wave function and a simple tensor product wave function. But it seems that none used this...